Semiexplicit K‐symplectic‐like methods with energy conservation for noncanonical Hamiltonian systems

Abstract

For the nonseparable noncanonical Hamiltonian systems, we propose efficient K‐symplectic‐like methods which are semiexplicit and energy‐preserving. By introducing two copies of the phase space and constructing an augmented Hamiltonian, we can separate the noncanonical Hamiltonian system into two explicitly integrable parts. Subsequently, explicit K‐symplectic methods can be constructed by using the splitting and composing method. To enforce constraints on the two copies of the phase space, we provide two transformations with energy conservation property. This enables us to obtain semiexplicit K‐symplectic‐like methods that preserve energy. Two algorithms are provided to implement the semiexplicit K‐symplectic‐like methods with energy conservation and their convergence has been proved. Numerical results on two noncanonical Hamiltonian systems demonstrate that the energy errors of our proposed methods remain bounded within machine precision over long time without exhibiting energy drift. Furthermore, the proposed methods exhibit superior computational efficiency compared to the canonicalized symplectic methods of the same order.